Abstract
The Jacobson radical of a ring R, denoted by rad R, is the intersection of the maximal left ideals of R. This notion is left-right symmetric; in particular, rad R is an ideal of R. A good way to understand rad R is to think of it as the ideal of elements annihilating all left (resp. right) simple R-modules. The Jacobson radical is also closely tied in with U(R), the group of units of R. In fact, rad R is the largest ideal R such that 1 + R ⊆ U(R).
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© 1995 Springer Science+Business Media New York
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Lam, T.Y. (1995). Jacobson Radical Theory. In: Exercises in Classical Ring Theory. Problem Books in Mathematics. Springer, New York, NY. https://doi.org/10.1007/978-1-4757-3987-9_2
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DOI: https://doi.org/10.1007/978-1-4757-3987-9_2
Publisher Name: Springer, New York, NY
Print ISBN: 978-1-4757-3989-3
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